Mixer update: Isolators gonna Isolate

I’ve been swimming in circuit diagrams for the past week, but I’m happy to say the mixer is progressing along nicely. At this stage I have on breadboard and working a line input stage, a headphone amplifier, and as of this afternoon the isolator EQ!

Line inputs and headphone amplifiers are pretty standard circuits and I won’t go in depth about them here. The headphone amplifier uses two 5532 stages in parallel for each channel, and provides more than enough power to drive my 63-ohm MDR-7506 headphones despite their low impedance. The Rane MP2016s implements something similar with a 33078, see that schematic for reference.

The isolator EQ is one of the key features of this mixer design that separates it from most of the DJ mixers out in the market. A traditional EQ is a resonant circuit that achieves its boost or cut in each band by changing how it resonates at certain pre-defined points. The graph below shows the frequency response of the Xone:32 EQ across its operating range. Its performance should be comparable to other mid-range DJ mixers on the market today.

Xone:32 EQ response. Taken from the Xone:32 User Manual.

Imagine you’re mixing in a track and you want to start by bringing in just the hi-hats. Cutting the LO and MID sections should leave you with just the HI, right? Well, not quite. You’ll get two big cuts of -26 dB at 50 Hz and at 1 kHz, since that’s where the LO and MID points are tuned, but have a look at the responses half way between them. Each curve cuts by about -5 dB at 220 Hz (where they cross), but combined that gives you only -10 dB cut at that point! All you wanted was your hi-hats, but you’ve got a big bump still making it through centered around 220 Hz.

Enter the isolator. The easiest way to think about an isolator is as a “full-kill EQ”. When you turn your bass and mid knobs to full cut, only the high frequencies will remain. An isolator is made from a bank of filters called a crossover that splits the incoming signal into three separate low, mid and high bands. These bands are then added back together with their respective volumes set by the EQ knobs. The plot below shows the responses of the low-, band- and high-pass filters used to make the isolator.

Frequency response of the crossover used to make the isolator EQ

The difference in design is subtle but important. Now cutting the lows and mids will have the effect of applying a true high-pass filter to the signal, rather than two sharp cuts with a rise in between. With the design above, our trouble point of 220 Hz with the Xone EQ is now cut by more than 40 dB, and the response has rolled off to about -62 dB at 50 Hz, where the previous best-case cut was -26 dB.

Not just any crossover will work to build an isolator — in particular, you need one whose bands add back together evenly and with consistent phase, called a Linkwitz-Riley crossover. Such a crossover can be built with any even order of filters, most commonly with cascaded Butterworth filters to give -24 dB/oct slope and -6 dB cut at the crossover frequency (the critical parameter for a flat summed response). A Linkwitz-Riley crossover is characterized by its order, with a fourth-order called LR-4, eighth order LR-8, etc.

After extensive ear-testing in Live I actually found the LR-4 to be a bit too drastic, for my tastes at least, so I built the crossover as an LR-2 with second-order sub-Bessel filters (Q = 0.5) with the appropriate phase corrections. With the LR-2, one output of each crossover stage must be inverted to maintain phase with the other. Since I used two crossover stages, I could either invert the middle band or both the low and the high bands to have everything sum linearly. Either way uses the same number of op-amps, so I chose to invert the lows and highs so that each band passes through the same number of stages.

Resistors and capacitors were chosen to give 250 Hz and 2.5 kHz crossover points. With the components I had on hand, it ended up being 267 Hz and 2.67 kHz. I used the free ESP Linkwitz-Riley calculator available here, it supports LR-2 and LR-4 designs. TL072 op-amps were used in the filter stages for their very high input impedance and 5532s were used for the summing stages given their superior noise performance. Notice how the Low and High bands are summed first with a unity-gain inverting amplifier to invert the signal and match phase with the Mid band.

The attenuating pots for each channel were 10k linear. It might seem weird, but it fits the way the knobs are set up. I wanted unity gain with the knob centered, a boost of 6 dB with the knob full right, and full cut to the left. Linear pots give -6 dB at 50% and full cut at 0% rotation, so add a gain stage somewhere in the signal path where headroom / noise makes sense and you’re good to go! Still to be determined where in my signal path that gain will actually be. To minimize op-amp stages the summing resistors are driven straight off the pot wipers, but it didn’t change the response much. With 10k pots and 47k summing resistors the attenuation at center only increases by 0.47 dB.